Finite Group Databasebeta

← #11779474

Subgroups — #11779474

Order 1152.

460 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593856C211yesmaximal, characteristic
2#10592549C211yesmaximal, characteristic
3#10590386C211yesmaximal, characteristic
4#10590283C211yesmaximal, characteristic
5C3×#4484C211yesmaximal, characteristic
6C3×#4481C211yesmaximal, characteristic
7#10589085C211yesmaximal, characteristic
8#68505—31nomaximal
9#68267—31nomaximal
10#64078C2211yescharacteristic
11C4×#634C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C3×C4×Dic6C2211yescharacteristic
14#63919—21no—
15#63918—21no—
16#63844—21no—
17#63843—21no—
18#63839—22no—
19C2×#3719—22no—
20C32×C4⋊C8C2211yescharacteristic
21#63645—21no—
22#63643—21no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25#63575—21no—
26#63566—21no—
27#5722—31no—
28Q8×Dic6—31no—
29#5092—31no—
30#5021—31no—
31#4850—31no—
32#4850—31no—
33#4850—31no—
34#4850—61no—
35#4699—31no—
36C3×#333—31no—
37C3×Q8⋊C8—31no—
38#4484—31no—
39#4484D311yescharacteristic
40#4481D311yescharacteristic
41#4456—31no—
42C2×#634—21no—
43C2×#634D411yescharacteristic
44C2×C3×Dic6D411yescharacteristic
45C2×C3×Dic6D412yes—
46C2×#627—22no—
47C2×C32×C8—21no—
48C32×C42C2311yescharacteristic
49C4⋊(C3⋊Dic3)—21no—
50C4⋊(C3⋊Dic3)—21no—
51C4⋊(C3⋊Dic3)D411yescharacteristic
52#3750—21no—
53C4×C3⋊Dic3—21no—
54C3×C4⋊Dic3—21no—
55C3×C4⋊Dic3—21no—
56C3×C4⋊Dic3D411yescharacteristic
57C3×Dic3⋊C4—21no—
58C3×C4×Dic3—21no—
59C2×C3×C3⋊C8—21no—
60C2×C3×C3⋊C8—21no—
61#3724—22no—
62Dic3⋊Dic3—22no—
63Dic32—22no—
64#3719—44no—
65#1633—91noSylow
66C3×C4⋊Q8—31no—
67C3×C4×Q8—31no—
68Q8×Dic3—61no—
69#944—62no—
70C2×#216—62no—
71C2×Dic12—62no—
72#888—61no—
73#888—61no—
74#888—62no—
75#888—61no—
76#887—61no—
77#887—61no—
78#869—31no—
79#869—31no—
80#869—61no—
81#869—61no—
82#869C2×D311yescharacteristic
83C4×Dic6—31no—
84C4×Dic6—31no—
85C4×Dic6—61no—
86C4×Dic6—61no—
87C4×Dic6C2×D311yescharacteristic
88C3×C4⋊C8—21no—
89C3×C4⋊C8—31no—
90C3×C4⋊C8C2×D311yescharacteristic
91C3×C4⋊C8C2×D311yescharacteristic
92C3×C4×C8—31no—
93#835—61no—
94#818—61no—
95#818—61no—
96#818—62no—
97#818—61no—
98#816—61no—
99#816—61no—
100#816—62no—
101#816—61no—
102#807—61no—
103C4⋊(C3⋊C8)C2×D311yescharacteristic
104C4×C3⋊C8C2×D311yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C3⋊Dic3—21no—
109C2×C3⋊Dic3—21no—
110C2×C3⋊Dic3—41no—
111#634—21no—
112#634—42no—
113#634Q1612yescomplemented
114C2×C3×Dic3—21no—
115C2×C3×Dic3—22no—
116C2×C3×Dic3—21no—
117C3×Dic6—21no—
118C3×Dic6—42no—
119C3×Dic6Q1612yescomplemented
120#627—82no—
121C32×C8—41no—
122C3×C3⋊C8—22no—
123C3×C3⋊C8—41no—
124Q82—91no—
125#494—91no—
126#477—91no—
127#477—91no—
128#333—31no—
129Q8⋊C8—31no—
130Q8⋊C8—91no—
131C2×C3×Q8—31no—
132C2×C3×Q8—32no—
133C2×Dic6—31no—
134C2×Dic6—31no—
135C2×Dic6—61no—
136C2×Dic6—61no—
137C2×Dic6—61no—
138C2×Dic6—62no—
139C2×Dic6—62no—
140C2×Dic6—121no—
141C2×Dic6D1211yescharacteristic
142C2×Dic6D1212yes—
143C2×C3×C8—22no—
144C2×C3×C8—21no—
145C2×C3×C8—21no—
146C2×C3×C8—61no—
147C2×C3×C8—61no—
148C3×C4⋊C4—31no—
149C3×C4⋊C4—61no—
150C3×C4⋊C4—61no—
151C3×C4⋊C4—61no—
152C3×C42—21no—
153C3×C42—61no—
154C3×C42C22×D311yescharacteristic
155C3×C42C22×D311yescharacteristic
156#216—124no—
157C4⋊Dic3—21no—
158C4⋊Dic3—21no—
159C4⋊Dic3—31no—
160C4⋊Dic3—31no—
161C4⋊Dic3—61no—
162C4⋊Dic3—62no—
163C4⋊Dic3—62no—
164C4⋊Dic3—61no—
165C4⋊Dic3—61no—
166C4⋊Dic3—61no—
167C4⋊Dic3—61no—
168C4⋊Dic3—121no—
169C4⋊Dic3D1211yescharacteristic
170Dic3⋊C4—21no—
171Dic3⋊C4—62no—
172Dic3⋊C4—62no—
173Dic3⋊C4—62no—
174Dic3⋊C4—61no—
175Dic3⋊C4—61no—
176Dic3⋊C4—121no—
177C4×Dic3—21no—
178C4×Dic3—62no—
179C4×Dic3—62no—
180C4×Dic3—61no—
181C4×Dic3—61no—
182C4×Dic3—121no—
183C2×C3⋊C8—21no—
184C2×C3⋊C8—21no—
185Dic12—124no—
186C22×C32#12011yescharacteristic
187C32×C4—21no—
188C32×C4C2×Q1611yescharacteristic
189C32×C4C2×Q1611yescharacteristic
190C32×C4#13711yescharacteristic
191C32×C4#13711yescharacteristic
192C3⋊Dic3—22no—
193C3⋊Dic3—41no—
194C3⋊Dic3—81no—
195C3×Dic3—22no—
196C3×Dic3—41no—
197C3×Dic3—42no—
198C2×Q16—182no—
199C4⋊Q8—31no—
200C4⋊Q8—91no—
201C4⋊Q8—181no—
202C4⋊Q8—181no—
203C4⋊Q8—182no—
204C4×Q8—31no—
205C4×Q8—91no—
206C4×Q8—181no—
207C4×Q8—181no—
208#107—181no—
209#107—181no—
210C4⋊C8—31no—
211C4⋊C8D3211yescharacteristic
212#103—181no—
213#103—181no—
214C4×C8—31no—
215C3×Q8—32no—
216C3×Q8—61no—
217C3×Q8—122no—
218C2×C3×C4—21no—
219C2×C3×C4—21no—
220C2×C3×C4—21no—
221C2×C3×C4—61no—
222C2×C3×C4—62no—
223C2×C3×C4—61no—
224C2×C3×C4C2×D1211yescharacteristic
225C2×C3×C4C2×D1211yescharacteristic
226C2×C3×C4D3×D411yescharacteristic
227C2×C3×C4D3×D411yescharacteristic
228C2×C3×C4D3×D411yescharacteristic
229C2×C3×C4D3×D411yescharacteristic
230C2×Dic3—21no—
231C2×Dic3—21no—
232C2×Dic3—22no—
233C2×Dic3—61no—
234C2×Dic3—61no—
235C2×Dic3—61no—
236C2×Dic3—61no—
237C2×Dic3—121no—
238C2×Dic3—121no—
239C2×Dic3—122no—
240C2×Dic3—121no—
241C2×Dic3—121no—
242Dic6—21no—
243Dic6—32no—
244Dic6—32no—
245Dic6—42no—
246Dic6—62no—
247Dic6—61no—
248Dic6—61no—
249Dic6—121no—
250Dic6—122no—
251Dic6—122no—
252Dic6—242no—
253Dic6—242no—
254Dic6—242no—
255Dic6Dic1212yescomplemented
256C3×C8—42no—
257C3×C8—41no—
258C3×C8—41no—
259C3×C8—62no—
260C3×C8—121no—
261C3⋊C8—22no—
262C3⋊C8—41no—
263C2×C32#45111yescharacteristic
264C2×C32#45111yescharacteristic
265C2×C32#45311yescharacteristic
266C2×Q8—31no—
267C2×Q8—32no—
268C2×Q8—91no—
269C2×Q8—182no—
270C2×Q8—181no—
271Q16—364no—
272C2×C8—21no—
273C2×C8—61no—
274C2×C8—61no—
275C4⋊C4—31no—
276C4⋊C4—61no—
277C4⋊C4—61no—
278C4⋊C4—61no—
279C4⋊C4—91no—
280C4⋊C4—182no—
281C4⋊C4—182no—
282C4⋊C4—181no—
283C4⋊C4—181no—
284C4⋊C4—181no—
285C42—61no—
286C42—182no—
287C42—181no—
288C42C2×D3211yescharacteristic
289C22×C3—21no—
290C22×C3#88211yescharacteristic
291C22×C3#88211yescharacteristic
292C3×C4—21no—
293C3×C4—21no—
294C3×C4—21no—
295C3×C4—21no—
296C3×C4—21no—
297C3×C4—21no—
298C3×C4—41no—
299C3×C4—62no—
300C3×C4—121no—
301C3×C4—122no—
302C3×C4C2×Dic1211yescharacteristic
303C3×C4#90911yescharacteristic
304C3×C4#91511yescharacteristic
305C3×C4#91511yescharacteristic
306C3×C4#91511yescharacteristic
307C3×C4D3×Q1611yescharacteristic
308C3×C4D3×Q1611yescharacteristic
309C3×C4D3×Q1611yescharacteristic
310Dic3—22no—
311Dic3—42no—
312Dic3—41no—
313Dic3—62no—
314Dic3—62no—
315Dic3—122no—
316Dic3—121no—
317Dic3—121no—
318Dic3—241no—
319Dic3—242no—
320Dic3—241no—
321Dic3—241no—
322C32#163311yescharacteristic, complemented, Sylow
323Q8—32no—
324Q8—61no—
325Q8—92no—
326Q8—122no—
327Q8—181no—
328Q8—362no—
329Q8—722no—
330C2×C4—61no—
331C2×C4—61no—
332C2×C4—62no—
333C2×C4—181no—
334C2×C4—181no—
335C2×C4—361no—
336C2×C4D3×D1211yescharacteristic
337C2×C4D3×D1211yescharacteristic
338C2×C4#381111yescharacteristic
339C8—41no—
340C8—62no—
341C8—121no—
342C2×C3—21no—
343C2×C3—21no—
344C2×C3—21no—
345C2×C3#473911yescharacteristic
346C2×C3#474711yescharacteristic
347C2×C3#480911yescharacteristic
348C2×C3#480911yescharacteristic
349C2×C3#480911yescharacteristic
350C2×C3#482211yescharacteristic
351C22#6392311yescharacteristic
352C4—21no—
353C4—62no—
354C4—122no—
355C4—121no—
356C4—182no—
357C4—361no—
358C4—721no—
359C4D3×Dic1211yescharacteristic
360C4#6380011yescharacteristic
361C4#6393111yescharacteristic
362C4#6394411yescharacteristic
363C3—21no—
364C3#6826711yescharacteristic, complemented
365C3#6850511yescharacteristic, complemented
366C2#1059060511yescharacteristic
367C2#1059095211yescharacteristic
368C2#1059101511yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socle, prime radicalC22×C32#120
hypercenterC4⋊C8D32
hypocenterC32#1633
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
113. #634Q16semidirect
119. C3×Dic6Q16semidirect
255. Dic6Dic12semidirect
322. C32#1633semidirect
364. C3#68267semidirect
365. C3#68505semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#105938562
#105925492
#105903862
#105902832
C3×#44842
C3×#44812
#105890852
#685053
#682673